An alternative analytic model that includes non-perturbative effects in the form of halo formation is the
halo model [1]}, [2]}, [3]}, [4]}.
The halo model assumes that all dark matter is tied up in gravitationally bound, non-overlapping halos, which have a prescribed density profile and an abundance set by the halo mass function.
Two-point matter correlators are computed by way of mean halo profiles integrated over the halo mass function and halo bias.
The halo model has seen success in the last few decades, and is used in modern analyses, albeit usually with some modifications, to model fully nonlinear scales (e.g. [5]}).
However, the halo model struggles in the so-called “transition regime” between the one-halo and two-halo terms.
The halo model also fails to ensure large-scale conservation laws are satisfied, and as a result cannot be completely correct in its original form [6]}.
Despite the successes of both PT and the halo model in complementary regimes, it is clear that neither of these analytic models alone are adequate to fully describe the nonlinear density field.
